"No. With a wallet, you have your private keys, all the crypto is completely yours.
With an exchange (any exchange, not just Binance) the exchange owns the crypto, they hold the private keys, it belongs to them. Your account is an entry in their accounting database that assigns some of the crypto to you. As you trade, those entries in the database get shuffled, but none of the transactions actually go on those respective coins' blockchains.
The reason for this is simple - in trading you want instantaneous transactions, not ones that take from minutes to hours."